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Mat. Sb., 1993, Volume 184, Number 4, Pages 61–104 (Mi msb980)  

This article is cited in 4 scientific papers (total in 4 papers)

Integral invariant lattices in Lie algebras of type $A_{p^m-1}$

K. S. Abdukhalikov


Abstract: Integral invariant lattices associated with the standard orthogonal decomposition of a Lie algebra of type $A_{p^m-1}$ are described up to similarity. Duality in the class of invariant lattices is studied. Even unimodular root-free lattices of dimension $p^{2m}-1$ are distinguished.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1994, 78:2, 447–478

Bibliographic databases:

UDC: 512.54+512.554
MSC: 17B05, 17B20
Received: 03.03.1992

Citation: K. S. Abdukhalikov, “Integral invariant lattices in Lie algebras of type $A_{p^m-1}$”, Mat. Sb., 184:4 (1993), 61–104; Russian Acad. Sci. Sb. Math., 78:2 (1994), 447–478

Citation in format AMSBIB
\Bibitem{Abd93}
\by K.~S.~Abdukhalikov
\paper Integral invariant lattices in Lie algebras of type $A_{p^m-1}$
\jour Mat. Sb.
\yr 1993
\vol 184
\issue 4
\pages 61--104
\mathnet{http://mi.mathnet.ru/msb980}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1225979}
\zmath{https://zbmath.org/?q=an:0819.17008}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1994
\vol 78
\issue 2
\pages 447--478
\crossref{https://doi.org/10.1070/SM1994v078n02ABEH003480}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1994PD76700012}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. K. S. Abdukhalikov, “Integral lattices associated with a finite affine group”, Russian Acad. Sci. Sb. Math., 83:2 (1995), 431–443  mathnet  crossref  mathscinet  zmath  isi
    2. K. S. Abdukhalikov, “Modular permutation representations of $\operatorname {PSL}(n,p)$”, Sb. Math., 188:8 (1997), 1107–1117  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. K. S. Abdukhalikov, “Automorphism groups of invariant lattices in the Steinberg module of groups of Lie type of odd characteristic”, Sb. Math., 189:9 (1998), 1273–1294  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. K. Abdukhalikov, “The Permutation Modules for Finite (Affine) General Linear Groups”, Journal of Mathematical Sciences (New York), 131:5 (2005), 5867  crossref  mathscinet  zmath
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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